In present work the NU method is extended for second order differential equations that have at most four singularities. This is carried out by changing the degrees of polynomials in the main equation of NU method. In this extended method \(\widetilde{\tau }(z)\)  will be a polynomial of at most second-degree, \(\sigma (z)\)  and \(\widetilde{\sigma }(z)\)  will be at most third and fourth-degrees respectively. Heun equation and confluent Heun equation can be given as examples for the equations that provide these boundary conditions of extended NU method. Heun differential equation and its confluent forms appear in several branches of physics. For a review see [1]}. Also a particular solution of Heun equation has been studied in Ref.[2]}.
